1,099 research outputs found
A scalar hyperbolic equation with GR-type non-linearity
We study a scalar hyperbolic partial differential equation with non-linear
terms similar to those of the equations of general relativity. The equation has
a number of non-trivial analytical solutions whose existence rely on a delicate
balance between linear and non-linear terms. We formulate two classes of
second-order accurate central-difference schemes, CFLN and MOL, for numerical
integration of this equation. Solutions produced by the schemes converge to
exact solutions at any fixed time when numerical resolution is increased.
However, in certain cases integration becomes asymptotically unstable when
is increased and resolution is kept fixed. This behavior is caused by subtle
changes in the balance between linear and non-linear terms when the equation is
discretized. Changes in the balance occur without violating second-order
accuracy of discretization. We thus demonstrate that a second-order accuracy
and convergence at finite do not guarantee a correct asymptotic behavior
and long-term numerical stability.
Accuracy and stability of integration are greatly improved by an exponential
transformation of the unknown variable.Comment: submitted to Class. Quantum Gra
The Thermonuclear Explosion Of Chandrasekhar Mass White Dwarfs
The flame born in the deep interior of a white dwarf that becomes a Type Ia
supernova is subject to several instabilities. We briefly review these
instabilities and the corresponding flame acceleration. We discuss the
conditions necessary for each of the currently proposed explosion mechanisms
and the attendant uncertainties. A grid of critical masses for detonation in
the range - g cm is calculated and its
sensitivity to composition explored. Prompt detonations are physically
improbable and appear unlikely on observational grounds. Simple deflagrations
require some means of boosting the flame speed beyond what currently exists in
the literature. ``Active turbulent combustion'' and multi-point ignition are
presented as two plausible ways of doing this. A deflagration that moves at the
``Sharp-Wheeler'' speed, , is calculated in one dimension
and shows that a healthy explosion is possible in a simple deflagration if the
front moves with the speed of the fastest floating bubbles. The relevance of
the transition to the ``distributed burning regime'' is discussed for delayed
detonations. No model emerges without difficulties, but detonation in the
distributed regime is plausible, will produce intermediate mass elements, and
warrants further study.Comment: 28 pages, 4 figures included, uses aaspp4.sty. Submitted to Ap
Flame Evolution During Type Ia Supernovae and the Deflagration Phase in the Gravitationally Confined Detonation Scenario
We develop an improved method for tracking the nuclear flame during the
deflagration phase of a Type Ia supernova, and apply it to study the variation
in outcomes expected from the gravitationally confined detonation (GCD)
paradigm. A simplified 3-stage burning model and a non-static ash state are
integrated with an artificially thickened advection-diffusion-reaction (ADR)
flame front in order to provide an accurate but highly efficient representation
of the energy release and electron capture in and after the unresolvable flame.
We demonstrate that both our ADR and energy release methods do not generate
significant acoustic noise, as has been a problem with previous ADR-based
schemes. We proceed to model aspects of the deflagration, particularly the role
of buoyancy of the hot ash, and find that our methods are reasonably
well-behaved with respect to numerical resolution. We show that if a detonation
occurs in material swept up by the material ejected by the first rising bubble
but gravitationally confined to the white dwarf (WD) surface (the GCD
paradigm), the density structure of the WD at detonation is systematically
correlated with the distance of the deflagration ignition point from the center
of the star. Coupled to a suitably stochastic ignition process, this
correlation may provide a plausible explanation for the variety of nickel
masses seen in Type Ia Supernovae.Comment: 14 pages, 10 figures, accepted to the Astrophysical Journa
Low Carbon Abundance in Type Ia Supernovae
We investigate the quantity and composition of unburned material in the outer
layers of three normal Type Ia supernovae (SNe Ia): 2000dn, 2002cr and 20 04bw.
Pristine matter from a white dwarf progenitor is expected to be a mixture of
oxygen and carbon in approximately equal abundance. Using near-infrared (NIR,
0.7-2.5 microns) spectra, we find that oxygen is abundant while carbon is
severely depleted with low upper limits in the outer third of the ejected mass.
Strong features from the OI line at rest wavelength = 0.7773 microns are
observed through a wide range of expansion velocities approx. 9,000 - 18,000
km/s. This large velocity domain corresponds to a physical region of the
supernova with a large radial depth. We show that the ionization of C and O
will be substantially the same in this region. CI lines in the NIR are expected
to be 7-50 times stronger than those from OI but there is only marginal
evidence of CI in the spectra and none of CII. We deduce that for these three
normal SNe Ia, oxygen is more abundant than carbon by factors of 100 - 1,000.
MgII is also detected in a velocity range similar to that of OI. The presence
of O and Mg combined with the absence of C indicates that for these SNe Ia,
nuclear burning has reached all but the extreme outer layers; any unburned
material must have expansion velocities greater than 18,000 km/s. This result
favors deflagration to detonation transition (DD) models over pure deflagration
models for SNe Ia.Comment: accepted for publication in Ap
Magnetization control of the nematicity direction and nodal points in a superconducting doped topological insulator
We study the effects of magnetization on the properties of the doped
topological insulator with nematic superconductivity. We found that the
direction of the in-plane magnetization fixes the direction of the nematicity
in the system. The chiral state is more favorable than the nematic state for
large values of out-of-plane magnetization. Overall, the critical temperature
of the nematic state is resilient against magnetization. We explore the
spectrum of the system with the pinned direction of the nematic order parameter
in details. Without magnetization, there is a full gap in the
spectrum. At strong enough out-of-plane or orthogonal in-plane
magnetization, the spectrum is closed at the nodal points that are split by the
magnetization. Flat Majorana surface states connect such split bulk nodal
points. Parallel magnetization lifts nodal points and opens a full gap in
the spectrum. We discuss relevant experiments and propose experimental
verifications of our theory
Topological relaxation of entangled flux lattices: Single vs collective line dynamics
A symbolic language allowing to solve statistical problems for the systems
with nonabelian braid-like topology in 2+1 dimensions is developed. The
approach is based on the similarity between growing braid and "heap of colored
pieces". As an application, the problem of a vortex glass transition in
high-T_c superconductors is re-examined on microscopic levelComment: 4 pages (revtex), 4 figure
Properties of four numerical schemes applied to a scalar nonlinear scalar wave equation with a GR-type nonlinearity
We study stability, dispersion and dissipation properties of four numerical
schemes (Iterative Crank-Nicolson, 3'rd and 4'th order Runge-Kutta and
Courant-Fredrichs-Levy Non-linear). By use of a Von Neumann analysis we study
the schemes applied to a scalar linear wave equation as well as a scalar
non-linear wave equation with a type of non-linearity present in GR-equations.
Numerical testing is done to verify analytic results. We find that the method
of lines (MOL) schemes are the most dispersive and dissipative schemes. The
Courant-Fredrichs-Levy Non-linear (CFLN) scheme is most accurate and least
dispersive and dissipative, but the absence of dissipation at Nyquist
frequency, if fact, puts it at a disadvantage in numerical simulation. Overall,
the 4'th order Runge-Kutta scheme, which has the least amount of dissipation
among the MOL schemes, seems to be the most suitable compromise between the
overall accuracy and damping at short wavelengths.Comment: 9 pages, 8 Postscript figure
Nematic Ordering of Rigid Rods in a Gravitational Field
The isotropic-to-nematic transition in an athermal solution of long rigid
rods subject to a gravitational (or centrifugal) field is theoretically
considered in the Onsager approximation. The new feature emerging in the
presence of gravity is a concentration gradient which coupled with the nematic
ordering. For rodlike molecules this effect becomes noticeable at centrifugal
acceleration g ~ 10^3--10^4 m/s^2, while for biological rodlike objects, such
as tobacco mosaic virus, TMV, the effect is important even for normal
gravitational acceleration conditions. Rods are concentrated near the bottom of
the vessel which sometimes leads to gravity induced nematic ordering. The
concentration range corresponding to phase separation increases with increasing
g. In the region of phase separation the local rod concentration, as well as
the order parameter, follow a step function with height.Comment: Full article http://prola.aps.org/abstract/PRE/v60/i3/p2973_
The Luminous and Carbon-Rich Supernova 2006gz: A Double Degenerate Merger?
Spectra and light curves of SN 2006gz show the strongest signature of
unburned carbon and one of the slowest fading light curves ever seen in a type
Ia event (Delta m_15 = 0.69 +/- 0.04). The early-time Si II velocity is low,
implying it was slowed by an envelope of unburned material. Our best estimate
of the luminosity implies M_V = -19.74 and the production of ~ 1.2 M_sun of
56Ni. This suggests a super-Chandrasekhar mass progenitor. A double degenerate
merger is consistent with these observations.Comment: Accepted for publication in ApJL (5 pages, 4 figures). UBVr'i' light
curves, UVOIR light curves, and spectra available at
http://www.cfa.harvard.edu/supernova/SN2006g
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